Textwrangler Open File in New Tab

Command + Option + [

or

Command + Option + ]

to navigate between open documents in the single window.

Forgive me if it this is off-topic, but have you tried Sublime Text yet? I used to use textwrangler, but I haven't looked back since I switched to Sublime. A must have for me is the multiple cursors, which I have not seen anywhere else. By the way, Sublime is not (technically) freeware, but they let you download and install it for free, just bugging you from time to time, asking you to buy, but without limiting any features. Off course, in case you adopt it it would be fair to purchase it, but if you are on a budget it is ok to postpone. Hope it helps.

I realize I'm necroposting a little, but to do this is BBEdit (which ate TextWrangler a while back):

When you have a file open, you want to use the View >>> Window Appearance >>> Show Sidebar menu option or hit Command-0 (zero).

Then profit. (See "Currently Open Documents" tab showing, below.)

Sublime is a great app, as is VIm, as is whatever Panic calls Coda next, as is WebStorm, as is VS Code, as is...

... but if you want to use BBEdit with tabs, that's how. ;^D